Modern LiDAR collection systems generate very large data sets approaching several million to billions of point samples per product. Compression techniques have been developed to help manage the large data sets. However, sparsifying LiDAR survey data by means other than random decimation remains largely unexplored. In contrast, surface model simplification algorithms are well-established, especially with respect to the complementary problem of surface reconstruction. Unfortunately, surface model simplification algorithms are often not directly applicable to LiDAR survey data due to the true 3D nature of the data sets. Further, LiDAR data is often attributed with additional user data that should be considered as potentially salient information. This paper makes the following main contributions in this area: (i) We generalize some features defined on spatial coordinates to arbitrary dimensions and extend these features to provide local multidimensional statistics. (ii) We propose an approach for sparsifying point clouds similar to mesh-free surface simplification that preserves saliency with respect to the multidimensional information content. (iii) We show direct application to LiDAR data and evaluate the benefits in terms of level of sparsity versus entropy.